Assuming that
32 pixels = 1 meter
1 soccer ball = 1 Kg

I would have to use ~11 N to move the ball, correct?
(disregard friction and all other modifiers for now)

Now, if I applied 15 N on the ball, the net force would be 5 N; how can I 'transform' N into speed/acceleration?
(We're supposing I am pushing the ball upwards)
I convert N to Kg, and then... what?

Any help would be greatly appreciated.
Any magnitude of force can accelerate the ball; there is no minimum force to move a ball unless you have static friction.

Force = Mass * Acceleration.

First, you have to figure out what the acceleration of the ball is (Force divided by Mass).

Remember, acceleration is the change in velocity per second (Thus meters per second per second), so you just do something along the lines of V += F/M (Per Force Vector component)

If you're also implementing impulses, keep in mind that acceleration is in square seconds. Make sure you make the proper unit conversions (I'm thinking from ticks to whatever the acceleration is in).

[EDIT]: I just realized what you're asking about is all along the vertical axis.

Unless you have the ball against a vertical surface, or you're implementing air resistance (which should be 0 when the ball is static), there's only two forces to take into consideration: The force you're applying and the force gravity is applying. You just need to find the net force by summing these two vectors up.

Then you can calculate the change in velocity via what I mentioned above.

It doesn't have to be ~11 newtons to accelerate the ball upwards. It just has to be anything above 10 newtons (And doesn't have to be an integer), so that the overall net force is upwards with a positive magnitude.